 Hello guys, it is five minutes out and I know some new people have come so I'm testing voice first of all Hello, this is voice also those of you who have not already click on this little box that I'm next to that has letters That says click to get a Q&A HUD You will get a little thing in a folder when you click on it I think it's just called QA HUD and if you right-click on that and select add it should put Letters a through F in the lower left of your screen And I will use this I only using it once during this talk, but this is a I Mean it's the clickers if you know what they are I use an analog version of this in my classes a lot In fact the color coding I chose from a through F this may be an apocryphal story, but you know that Supposedly the standard gauge for train tracks can be traced back to the width of carts and Roman times Because that was the size of the ruts in the roads That all of Europe had because Rome kind of spread out through all of Europe Well, so similarly the colors I use for color coding this is a little bit vestigial to The cards I use in class where I have students hold up cards in Response to questions that I ask and I color code them So that I can just quickly look and by color I can see what answers people have I don't have to necessarily look at the letters and The colors I chose were because well, I just went to staples and thought okay What colors of card stock can I get to print on and I got six colors that looks different enough from each other? And that's these were the six colors and so now I've been sort of reverse engineering back To use the same colors so in the slides I put online or not online But in my presentations I use in class I color code the answers like a b c d e and f not the text of the answers But just the letters to match the colors on the Cards that the students have because I'm anal that way so now when I made the thing in second life I color coded it the same way. Anyway, in case you were wondering where the colors from I'm pretty sure you didn't care Blood it was a voice test. So there you go. I Yeah, we're still a few minutes early, so I won't start right away I'm just sitting here blathering away Because that's what I do. I'll see. I mean, I actually sort of just hacked this together Mostly yesterday. And so the presenter HUD is very rudimentary. Basically. I have to manually control it all I'll make the presenter had better with time so that maybe if other people want to try and use it It'll be usable right now I have to manually type in each question, but I'm thinking I'll set it up So you could give it a note card of questions if you want to have Preset questions that you're going to go through or something like that. So we'll do another voice test since Yeah, I will explain the HUD When we get closer to it, I'll just say right now Basically, you should see six letters on the lower left of your screen and they won't do anything yet at some point I will Ask a question and at that point the question will show up as floating text on your screen above the HUD and then You can click one of the answers and it'll send the answer back into me and we'll look later and see what all the answers everybody said But for now the HUD is just sitting there doing nothing. It's actually listening It's waiting to hear for a question from my little control thing which I have on my HUD, but No question is active right now So I won't do anything. Let's go ahead and do a test. We're not just for fun. So everybody Let's see how it works Attach the HUD you should see the six colored letters and the lower left to your screen if you don't have one touch it here Touch this big box and you'll get a folder with the HUD in it And then you can right-click on it in your inventory and select add it will show up in the lower left of your screen Once you've done that I'm going to go ahead and send out a question Now you should see on your HUD it should tell you what the question is and it should say in blue that the question is open so if you click on the HUD and if everything works it'll send your answer to me and I'll start to see what is happening Where I have a channel listener text. Yes. So I've got a couple of answers already. So everyone Yeah, if you feel like it go ahead and answer. What is your favorite letter? the question should It came in chat That's interesting. Well, it should have shown up on your and it should still show up on your On your little HUD it should be floating text over it So if you do you have some sort of channel listener up or something like that? Very interesting that you're not getting it Do you see the six letters on the lower left side of your screen? Listener is spamming the chat. Oh, yeah that channel listeners But that was something I had on myself that I have taken off That's interesting that you're not getting the question I think it should be shouting it to the whole You've got the HUD up So what it is is as long as the question is open it keeps oh if it shows above the HUD Yes, so Sean tall sees it above the HUD. So you should see it above the HUD above the letters on your You have attached it to your HUD. Yes. Okay Interesting it's not working for a bunch of people and I don't know why Oh, I know why It looks like scripts are disabled in the region Oh, no those belonging to the landowner should my scripts work here shunt all What is attached as a green ball at top center of screen? Okay, HUD should not be a green ball at the top center of the screen the HUD should be um right Okay, good right click on the um Yeah, white text above the HUD is where you should see it So right click on the the HUD that you got from this box. It's just qa HUD is the name of it right click On that in your inventory and select add and then the letters will show up on your screen not Here on the box, but just in front of everything on your screen right as a hub Um You're being no question above it. Okay. Well, some things are broken. I'm going to have to do more testing of this Uh to figure out why it's not working. So I've tested it with two people before And evidently it's not working. So I only see three answers How many of you do see the question above it? Um, well, you may have clicked on it without realizing it Let's see If you and if you see the question you picked one of them There it says your answer is b But he has answered b Yeah, this is the other thing you may have other things on your screen that are blocking it You may have to right click on it and edit and move it around to see the thing Four answers that have come in now I don't think it's working very well. Um, yeah, if you have the six letters, but you don't Is there a question floating in text above it or b? Yeah, I see that yeah, so um, I see that there's no question I know some people have a question some people don't and I don't know what the difference is why some people do and some people don't Oh, let me check a thing here start over open No, it is a region say question chan It should be working um, you do all right, so When you accept the HUD it just goes into your inventory. You have to then open your inventory find the folder you got Right click and add it Yeah, so the HUD The HUD When when you click on it all we'll do is change what answer you have at the bottom Assuming that there is a question that's open Now for their for the question to be open and what happens my thing is every five seconds sending out that the question is opening So if you attach it Within five seconds you should have above it White text saying question open or question colon. You don't need to wear the group tag You should just be able to just attach it and have it work Inventory you find qa HUD right click on that select add It'll show up on your screen Able for you, but they should still work because I wrote this script And a question. Yeah, so if you have the question. Oh, that's interesting. I wonder if If the tag you've got the question, you know what there must be something about um attachments in scripts not working if Yeah, I bet that's what it is I bet that's something like that because the people it was working for before I think were people that We're not working. Yeah, so If it's working go ahead and click on what your favorite letter is I have eight answers now. I bet there was something about the script settings that was interfering with it So we'll have to think about the right way to do that Have to get some people in here at some point. Yeah, so you need the group tag interesting I don't I'm not completely clear on how things are supposed to work Anyway, all right. Well, I'm going to start the real talk. So I'm going to go ahead and close the question So at this point those of you with the HUD should just see um last question and what your answer was and We'll see here that Nobody likes the letter d and I feel very sad for the letter d because of that Two people like a b and c and one person likes f So those are the answers that we got. All right. Well, we'll try this a little bit later We're going to have another chance to try the HUD a little later in the talk But for now, I'm going to start talking about entropy Um entropy what is entropy? Turns out not to be all that an easy question. This is one of those things that Most people who are even a little bit culturally literate if you ask that question, they have a quick answer for you And then if you poke at the answer they gave you Maybe they start to realize that they don't know exactly what they just said so um I want to talk about what entropy is now the picture I put on the front I started with a mushroom cloud here This is actually a volcanic eruption um What does that have to do with entropy? Well, this is an event that produces a whole bunch of entropy increases the entropy of the universe That turns out pretty much every physical process does that so I could have shown almost anything But I'm also right now My wife gave me for Christmas the trilogy the broken earth trilogy from nk jemisin Which is the one that won the hugo award all of the last three years in a row It's actually quite good and that's all about volcanoes and earthquakes and stuff So I figured I'd put a volcano on here because why not it's entropy So When I was in college I took a statistical mechanics class from Dave beeman who by the way Um is a little bit famous because you can search for beeman's algorithm on wikipedia And it'll give you a differential equation solving method that is named after him He was a little bemused that it got named after him But he taught my statistical mechanics class and he said more he didn't exactly say this because he said the whole word out More bs has been written about entropy than any other physical quantity Um, and this may well be true because entropy is one of those things that sounds so cool Um, and so then people start saying things about it But then people easily jump to wrong conclusions about what it says now I think Dave is probably wrong. Well, maybe not physical quantity I think the thing in physics that the most bs has been written about is the collapse of the wave function. Oh my goodness The amount of bs that's associated with quantum mechanics and the collapse of the wave function is just out of hand But there's a lot of bs out there associated with entropy So what we want to do is think about what is entropy now my guess is I um, I was talking I had a class this year where I talked in the class What does entropy ask getting the students say with great confidence entropy is disorder say well, okay And what does that mean? And that's kind of a turns out to be a harder question to ask answer than you might think Well, all right Many of you yes entropy is the dreaded s in physics classes In fact, here is that very dreaded s on the screen in front of you the second law of thermodynamics Which is a you know, if you talk about physics laws that people have heard Um, e equals mc squared is probably the first one that they've heard if they've heard of any But a lot of people have heard of the second law of thermodynamics and the second law of thermodynamics If you're uh, if you like the the most concise way of doing it, you just describe it here as delta s is greater than or equal to zero Um What does this mean? Well, it says in any closed system also sometimes called any isolated system the total Entropy of the system will never decrease Well, okay, so entropy always increases. That's what the second law of thermodynamics says entropy always increases There's a few things about this first of all It's very important that this is a closed system and a lot of the things people get wrong about entropy is forgetting the fact That if you have other systems that you're interacting with it's entirely possible for your own entropy to go down Like for example, you look at living beings We are highly ordered organisms and you would think well, how could this have happened? We've reduced all this entropy that doesn't make sense Well, how has it happened? It turns out we're gigantic entropy producers Because we produce heat all the time and all that weight heat carries off All kinds of entropy with it Yeah, so vick or phil depending on how you want to describe him says entropy is why nothing lasts forever Um, and that's what's on the bottom here processes tend to be irreversible Um In the jargon of this a reversible process is a process whose change in entropy is zero So if you go through a process and the entropy Changes zero you can go backwards and you're still okay and in chemistry There's the Carnot cycle, which is the the maximally efficient heat engine It's a purely theoretical construct because you can't really build it in reality But it is the maximally theoretically possible efficient heat engine Um, or at least one of them. There's other ways you can describe it It's a reversible process, but Almost always it's not delta s equals zero delta s is greater than zero and if delta s is greater than zero It's impossible to go back to where you started Because the entropy has increased and to go back where you started you would have to decrease the entropy again And you can't do that now That being said Well, okay, not that being said I want to say one more thing first of all almost every Almost every process that happens is irreversible Interesting about this though is that on the most fundamental physical level there is no such thing as entropy Uh, there's also no such thing as temperature which sometimes surprises people if you're talking very basic fundamental particle physics entropy If you're just talking two particles interacting with each other entropy isn't really a thing You need to have a statistical quantity of stuff before entropy is a thing And even in pure classical mechanics you can at least imagine a perfectly reversible process So if you have a bouncing ball with a perfectly elastic collision So every time it bounces off the ground it comes back up to exactly the same height it started at That turns out to be a perfectly reversible process entropy is not increasing all of that sort of thing but um In practice that it really happens with bouncing balls You know if you bounce a ball it doesn't come up as high as it started what happened Well, some energy got lost It would have needed to keep all of its mechanical energy to bounce as high as it went Where did that energy go? Well and the ball bounced off the ground the ball deformed And that tended to heat up the ball a little bit and that thermal energy has more entropy than just the bulk motion of the ball and so Okay, actually the entropy increased every time the ball bounces off the ground It heats up a little bit and then it radiates away that heat and all of those things cause the entropy to increase So fundamental physical processes very basic processes can be reversible, but once you get macroscopic It's almost inevitable that you'll have an irreversible process Right. So that's so the second law of thermodynamics says entropy always increases. That's great But that doesn't answer what entropy it is. It just says, oh, this is a thing that has to go up But what is it? Well, again, we come back to disorder Well, all right, let me give you a different definition and this is closer to the the chemistry definition or the thermodynamic definition of entropy Um, and that is I want to talk about the notion of free energy Which sounds awesome. Doesn't it, you know, hey energy, it's free. Well, okay. That's not really what it means here Energy is energy turns out to be a really complicated and difficult concept But don't think about it too hard. You kind of know what it is um energy is I don't know It's a thing. I don't want to try and define it because I'll probably do it wrong, but energy Well, there's various different forms of energy. There's potential energy if you hold something above the ground There's kinetic energy if something's moving. There's thermal energy and that's the energy something has just because it's hot It's the vibrations of all of the air molecules or Person molecules or whatever it is that the thing is made out of There's other forms of energy. There's electrical potential energy We often will group a bunch of the energy together and just call it internal energy So in these equations here where you see you That just means internal energy and we keep it nice and abstract. It could be the energy that's available because you have some atoms that could potentially interact with other atoms and energy could be released It could be internal thermal energy if you have some way of getting it out something like that um But that's internal energy. Well, so if you look at this this here is the Gibbs free energy This is the hem halts free energy and I want to start with hem halts free energy because it's actually a little easier to think about Hem halts free energy is defined as the energy minus the temperature times the entropy And if you just think about all right, what does that mean? Well, you have a certain amount of energy and why do you care? What do you want to do with energy? Well, one thing you might want to do with energy is do work and what does work means it means pushing things around Really so think about a steam engine you um You cook your coal you light your coal on fire to heat up some steam to move some turbines to push your train around That's that's so you're doing work. You're pushing things around Well, all right as you do this the entropy is going to increase And as the entropy increases the free energy decreases so the amount of energy Total energy overall is conserved now of course this you know This internal energy may go to other places and that's where you might bring in the Gibbs free energy Where if you're talking about a gas you can have the pressure and the volume And if you one way to think about moving things is changing the volume imagine like a piston and a car engine As the gas explodes it pushes the piston out which increases the volume of the chamber that the gas is in um Well, all right, so all that energy is conserved But then as entropy goes up the total amount of Gibbs free energy goes down And what mike just said is that Gibbs free energy is the amount of energy available to do work And so as entropy goes up you have less and less energy available to do work And so this is another way of thinking about entropy is that entropy Basically tells you how much energy in your system is in a form that can no longer do useful work How much thermal it's it's defined as thermal energy per unit temperature So that's why you notice that you multiply by temperature and you get energy That is there that can no longer do useful work Okay, and that's great and that shows up in equations like this and there's a whole bunch of other thermodynamic equations that we could Whip out which i'm not going to whip out but you could whip out the entropy shows up in That describes as physical processes occur. Here's how the entropy changes and as the entropy changes The energy goes more and more into a form where it's very difficult to do anything with it Well, okay, that's good. That's pretty technical, but that is a good technical working definition of entropy entropy is A measure of the amount of energy that Is thermal energy in a form that's no longer easy to do work with Now energy conservation and that by this I don't mean well, okay, let's talk about energy conservation if your um environmentally conscious and or economically conscious and you want to conserve energy That turns out you don't have to worry about it because one one of the fundamental physical laws that seems to apply to every theory of physics that we have come up with that has any bearing on reality is Energy is conserved. You can neither create it nor destroy it You can change it from one form to another but the total amount of energy and any closed system always stays the same Oh, so why do we have to worry about conservation of energy? It turns out when we talk about conservation of energy Think about what you mean. It means like having a more Fuel efficient car so you use less gas to go a certain distance What you're really doing is trying to conserve entropy Or conserve lack of entropy. You're trying to keep entropy from going up too fast when we talk about conservation of energy That's what we really mean We want to keep as much energy as possible in a usable form and avoid having it go into the unusable high entropy form All right, so that's another way of thinking about entropy But that still doesn't get it at least what I as a physicist think is the most fundamental definition of energy of entropy And that gets at the whole disorder thing So entropy is disorder if you ask people What? um Entropy is they often say entropy is disorder and then they will Maybe look at a picture like this one. I don't know. There was a podcast um I'm blanking on the name of the guy who did the podcast, but I'm sure shantel will Tell us momentarily in chat Um, I interviewed I did just the other day and they we were talking about this talk and he mentioned his sock drawer Um It's easy to think I see even been hooked. Thank you. It's easy to think about entropy in your sock drawer because you're supposed you're anal retentive and you line up all of your socks So that they're all vertically oriented and you have them all right next to each other So that matching socks are next to each other. They're easy to find it's very organized And then all of a sudden you need the black socks that are at the back underneath So you dig into it you shove things aside you find the black socks you come back later And your sock drawer is a bit of a mess and then you look for the next pair of socks Or you do the laundry and you put them back and you're not keeping it organized the next thing You know what your sock drawer is a mess and it's hard to find anything It's disorder your sock drawer has a higher entropy state than it used to um It's the same sort of thing here This this picture which I uh, I searched for entropy on only if matching socks matter That's an important point actually that if you're willing to wear non matching socks then you know go you You're you're not caught up by the strictures of society Um if you search for entropy on wiki media commons, this is one of the pictures you get which I think is a very nice picture Here here's this guy Alex Dino vitzer supposedly who has a box of capacitors and presumably yet another box of capacitors that he dumped out and here You can kind of see that oh look, they're all blue here and they're all brown. He's Separated his capacitors by their capacitance and other things, but then when he's dumped them out, it's a big mess and so These capacitors are in a higher entropy state than this It's disorder and okay You can get some intuitive sense for what that means Um, there's other examples, um one of the classic ones if you drop and break a mug So you have a mug. It's in a high order state. It's just uh, you know, it's a mug It looks good. You drop it on the floor now. It's fragments. It is way harder to reassemble it Maybe impossible to perfectly re reassemble it then it was to break it in the first place And it turns out in reassembling it you're going to do things like use up glue and probably heat and raise entropy other places So the broken mug has much more entropy than the mug that's all still together Okay, so that's another idea of disorder But um, no they're no they're not all at the same entropy state If you just look at the entropy of the mug itself when it's broken It's in a higher entropy state and I can give you the definition that'll make it clear a little a little bit later, um now You may argue though. It's like, wait a minute. You said in every physical process Entropy always increases and then I talked about the sock drawer But you always have the option of reorganizing your sock drawer, right? You can sit down and reorder your sock drawer and then it's nice again So the entropy of your sock drawer went down. How can that be? Well, again, your sock drawer is not a closed system because you were in there interacting with it And you were thinking about it and you were moving socks around to get them all organized So yes, the entropy of your sock drawer itself can go down But not if it's an isolated system So what that means is that when the entropy of the sock drawer went down entropy somewhere else went up And where's that going to be? Well, probably a lot of it It's going to be in the heat of you moving your muscles around things like that one of the jokes we used to make Phil was talking earlier about how his desk is a High entropy system some people have joked that if you see one of those desks like that and you come back later And they've reorganized your desk. So it's all nice and neat and clean You say, oh my god, some major civilization somewhere just went extinct to keep the entropy of the universe in balance Um, well, okay So what does it really mean to say that some entropy is disorder? And that's what I want to try and get at next And to get at that we are going to start talking about statistical mechanics Which is one of the great achievements of 19th century physics. It's All right, so mechanics how does stuff move around? Newtonian mechanics is sort of the basic laws of classical physics That newton figured out and that people messed with for a long time And that we still use to describe how most of the things move around and our universe and our solar system on our planet Great stuff statistical mechanics is what happens when you have too many particles to track all of them all at once So this is great if you have An earth orbiting a sun Um, yeah, newtonian mechanics is fine You don't have to worry about statistical mechanics as you have two things But what happens when you're talking about all the particles in a gas? Well, you know 22.7 liters of gas has 6.02 times 10 to the 23rd molecules in it That's way too many to try and track each and every one at all times So statistical mechanics is um the science that lets us talk about how all those kinds of things work And there are two very important concepts and statistical mechanics. These are a little tricky So I'm going to spend a little bit of time trying to get them across The concepts are micro states and macro states So first of all when I talk about the state of the system basically that means what is its deal What are the things you need to specify to describe? What the system is like the state of the system. So if you just have one Ball at the end of a spring attached to the wall You can Completely specify the state of the system by saying where is the ball and how fast is it moving? That'll let you then figure out how stretched the spring is you can do all kinds of stuff with that So the state of the system is what things do you have to specify in order to know what you need to know about the system? Well in statistical mechanics, we actually divide that into two separate concepts One is the macro state and so think about macro versus micro Macro state is what do you use to describe the system as a whole? So if you're talking about gas It could be things like the density profile. I guess the gas, you know, if you look at the atmosphere of the earth It's higher density at sea level than it is up at a mile up So that's what I mean by density profile. Not just what is the density, but how does it change your position? What is the temperature or really the temperature profile? What is the pressure things like that all those variables describe the gas as a whole So that is what I mean by macro state. It's the macroscopic state Whereas the micro state is the full details of all the particles and where they all are So the micro state is way more complicated to specify because again, think of how many molecules there are And 23 liters of gas There's almost 10 to the 24 and that's such a big number that we don't even have words for it, right? It's like a kind of even do this. It's a Million billion billion if I did it right except I think it's actually 100,000 billion whatever it doesn't matter 10 to the 24. It's a big number That's a lot of things you have to specify the positions and the velocities of all Of those all of those particles Yes, and vic is also saying quantum physics as we can only give a probability for the micro state That is true. In fact, it turns out. It's only a probability for the macro state But those probabilities turn out to be really really really sharply peak. So it doesn't matter But this is true even in classical physics. You don't even need quantum mechanics from micro state to be something that's incredibly hard to specify Microscopes don't look at microstates. Microscopes look at small things So micro here is supposed to remind you of small, but it doesn't mean oh, it is small It just means All the details whereas macro means the overall general idea of the system So and I will give you an example in a moment with all the with the much-vaunted dice to see what's the difference between a micro state and a macro state But so the concepts are important macro state What's the overall state of the system? What's its pressure? What's its density? What's its temperature? Micro state? Where are all of the particles? Where are all the gas molecules? And how fast are they moving in which direction? Now here is the fundamental assumption of statistical mechanics says All physically possible Microstates are equally probable now what I mean by physically possible Is that we do have some basic laws things like conservation of energy and conservation of momentum that? Will limit what states you can even have so if you have a closed system um And that system has a certain amount of momentum say it's at rest there's no momentum You can't have all of the particles going in one direction because that would have a different momentum From what the momentum of the state as a whole has so not every single conceivable micro state is physically possible, but There tend to be a bunch of different micro states that are all physically possible um, and all of them are equally probable um, yeah, and so then Now here's the thing is that all those all those very um Large number of micro states may correspond to different macro states and to try and make this more concrete. I want to talk about dice All right, so let's talk about dice. First of all In this analogy system. What is physically possible? Well, I'm going to define a physical physically possible state We're going to roll three dice where each die is sitting On the ground, so we're going to wait until the dice are done rolling each guys is sitting on the ground with one face unambiguously pointing up That's a physical possible state So we're not going to count states where dice land on there on the corner or anything like that, right? That's not going to be a final stable state. That's not going to be something That's not one of the states. We're including all right. That's what a physically possible state is Then the micro state of dice Is just one of the values on each die And I'm making the assumption that we can tell the dice apart one of the things that comes into quantum mechanics is that Particles become indistinguishable. You can't tell them apart and that adds some complications that I'm not going to go into So we're going to assume you can tell the dice apart. So in this case, I rolled three dice Here's what I got The micro state I have to specify the state of each and every individual particle. Well in this case, there's three particles So the state of the red die is three the state of the green die is two the state of the yellow die is four That is the micro state of the system Right, you need three numbers to specify the micro state of the system What is the number on each die? But then the macro state is just the sum of all the values showing on the three dice That's what the macro state of the system is. So in this case, the macro state is nine I only need one number to specify the macro state. And so here's what I'm going to do I'm going to start rolling large number of dice and I'm going to Pull this little thing out here that's going to keep track for us How often various different macro states show up? So you'll notice at the center of the Arena here, there's a little pyramid and when I click on it, it's going to throw three dice And we'll see how well this works with all the people here And when the things finally stop rolling around, you notice there's two fives and a three So the micro state is five five three and the macro state is 13 And so once the dice stop rolling around eventually it counts. Oh look, we had macro state 13 And so my little histogram here will count. Oh, we had a 13 and it counts up a 13 And that's great. And eventually the dice disappear. So now what I'm going to do is I'm going to roll a large number of dice Now hopefully we agree that these are fair dice Or at least the physics engine in second life is fair It's equally probable for each die to give a one two three four five or six And then we've got three of them. So all the various micro states all the possible permutations of the dice having different values are equally probable And so I'm going to start rolling a whole lot of dice and we're going to see what happens It's going to be colorful is one thing that will happen Rolls the dice and you'll notice when I throw them out They all spin and I have it so they all get a kick when they first come out to randomly Roll and so yes, some of you may get hit by dice and if that happens, I apologize I'm getting hit by dice myself here. We tried to Clear out the ground level so that nobody would be sitting down here where the dice were all going to fall And I'm just going to keep clicking on this and we're going to see the dice come out And if you're really fast you can track all three dice of one color and see what the number was But it's probably really hard To track that because they're coming out awfully fast But fortunately we have my little histogram thing here to track it for us and it is counting how often we get various macro states And now there's another thing that a whole nother talk I could give us about the statistics of small numbers I have to roll a whole lot of dice for this really to work. Well, ideally I should roll dice a hundred times We'll see if I can get today But you'll notice over here. Okay. I'm getting lots of different possible numbers And as the dice settle down, you can see that the the bars on the bar graph go up a little bit And it counts how often I'm getting various things Here comes some pretty pink dice and some nice purple dice Slightly different shade of purple dice. The way I wrote this is I just randomly generate the colors I have a sort of minimum red green and blue So that they don't come out black and you can't read the tips, but um, I have a um Yeah, I have um A randomly generated the colors and then the dice shout to the histogram thing what their colors are Um, yeah, they just may not be resin fast enough Um for you to see them and so the other thing people will be noticing is that once the dice stop moving They've got about 10 seconds left to live and then they disappear Which is good because otherwise we would all be hit deep in dice right now um And so what happens is the dice roll around and they check themselves um And when they have figured out that they're still they shout what value they are over to the histogram thing And the histogram thing goes and counts up all the dice of the same color and once it's got three of them it increments it so Yeah, so bergen makes an important point. That's like you have to iterate the experiment many many times In order to actually really get a real sense of the outcome and that is again. This is the statistics thing um statistics of small numbers is always hazardous because Randa if you only roll a few dice you could randomly say oh look I rolled three days I got three that means three is really probable although look here you notice I've rolled a whole bunch of dice now And we have yet to get either a three or a four which tells you Three and four must not be all that common now interesting the 11 doesn't seem to be all that common either But it really ought to be so we're still in the statistics of small numbers regime I'm going to keep rolling dice partly because I like watching all the dice bounce around It's it's soothing. It's a little like a lava lamp Let's see if I can crash the whole region by clicking too fast. I think it just Refuses to hear the clicks if I click too fast it seems Uh seven and 11 are magic numbers and craps But that's just the rules of the game It turns out when you roll two dice seven is the most probable result 11 is not The snake eyes is bad. So, you know, it's very interesting. It looks like I'm seeing slightly biased dice here But again statistics us why would they choose 11? I have no idea I don't know who wrote the game and why they chose it Yeah, it does suggest although, you know what I bet if we rolled this enough it would uh It would it would work itself out because there's no reason I can imagine well All right, there is a reason why it might be biased and that is the dice do have a natural Um They have a natural not a natural but a starting Direction I forget which way it is When they first come out they're in a certain direction now I try to randomize that by making them all roll and so that should take care of it But whatever and yeah, this is Mike makes a very valuable point Grades from large classes. You never have enough students even with 100 students to get a perfect bell curve Right, so I'm gonna I'll stop here. We're getting a sense of what's going on here You will notice Well, you know You will notice here that we have almost no threes fours 17s or 18s We have a whole lot of 10s and 12s and we should have a whole lot of 11s, but okay, whatever You get a lot of results in the middle And not very many results on the outside Um, it's a classic bell curve All right, so let's think about what this means what this means is If each and every micro state is equally possible So I'm just as likely to get a 111 as I am a 532 on the three dice in order That says that a whole bunch more of the micro states give you 10 than give you three whole bunch more Dice show up where the sum is 10 than you do when the sum is three now and fixing maybe there's some harmonics And this is you know, this is this is one of those things that happens You start to see patterns humans are really good at seeing patterns. We evolved to see patterns We do it so well that we see them even when they're not really there And I think that's just because evolutionarily It is better to jump at the saber tooth tiger That is not in the bushes than it is to not jump at the one that really is there So yes Um, anyway, yeah, so um much more often Many more of the micro states give you 10 Then give you three many more of the mice, right? So 10 Is a much more probable macro state than three is even though all the micro states Are equally probable the macro state 10 is much more probable than the micro state three That's what we saw by rolling these dice and you can actually work this out without doing the random rolling of the dice I'll give you an example of that. I'm going to move this guy back out of the way here um If we go to the next slide Um, and if you look at what are the possible ways of getting various different macro states Well, let's just talk about three and five There is only one way to get macro state three and that's if all three dice show up one That's the only way you're going to get a sum of three Whereas if you want to get a sum of five, there's actually six different ways to do it All right, and I've shown them here and notice you can tell the dice apart So this one one three and this one one three are actually different micro states Because here it's the green dye that's three and over here. It's the yellow dye that's three So there are six different micro states Or six different ways you could roll the dice where the total is five And if you work out all of the possibilities it turns out that 10 and 11 are the most probable There are 27 different ways You could roll the dice and have the sum come up to 10 right So if you think about what this means All the micro states are equally probable But this says that macro state Of the sum of the dice being five should be six times more probable than micro state three Because all the micro states are equally probable. Well, there's six of them that give you this and only one of them that give you this So are you saying, okay? Well, that's great. How does this come into entropy? Well entropy Is a measure of the number of micro states that goes along with your macro state All right, and so i'm about to give you the equation entropy The entropy of a given macro state Is equal to this same boltzmann's constant times the natural log and don't worry about the natural log We'll come back to that in a moment It's a thing you could do times omega where omega is the number of micro states available to the system all right, so The number so for a given macro state, how many micro states Do you have? Count them all up. That's what omega is now. You may worry a little bit saying wait a minute when you're talking about classical particles What is the number of different places that a molecule could be because it's continuous? Sorry, we have ways we'll just say we have ways of dealing with that with integrals and the letter h and stuff And don't worry about it too much. Think about the dice right think about the dice omega is the number of different ways That you can get a given macro state. So if you want to get A macro state of the sum being three omega is one there is only one way to get that whereas if you want The macro state to be five there are six different ways of doing it So that's what capital omega is here it would be six In the case of macro state five and one in the case of macro state three And then entropy is just how many micro states are available at a given macro state And this you start to get a sense of why entropy might increase because The more micro states that are available the more probable that macro state is so whatever if I have dice and I look at them So so you put three dice In a pan and look at what they are and actually set them all to one one one one So there's some three shake the pan look where they fall shake the pan look where they fall Shake the pan look where they fall do it over and over and over over again And you will much more often see them show up 10 11 than three again So that's an entropy increasing thing every time you shake the pan Um, you you alter the system. It's much more likely to go to a higher entropy state than a lower entropy state And then boltzmann's constant is just a thing that we multiply it by to give it the right units in terms of energy and temperature and stuff at some level what boltzmann's constant really is Is the conversion factor between the units we have chosen to use for temperature and units of thermal energy Okay, whatever it's just you can just take it as a given that this is a constant we multiply by what's really important here Is that entropy is this natural log of the number of states And the reason we take a natural log one of the things that have basically what a log is A log base 10 is to what power do I have to raise raise 10? In order to get the number so 100 I have to raise 10s at the power two in order to get 100 So the log of 100 is Two All right the log base 10 and so it's a way of saying, you know What powers do you have to raise things to it's really useful when you have really freaking huge numbers Which you do with possible states of systems When you have a gas with 10 to the 23rd particles in it the number of possible states is ginormous And so logarithms become very useful and keeping your numbers from getting too terribly out of control So for the dice and here i'll give you the example for the dice Um here are the various states The various macro states three through 18 of the possible macro states of dice Omega is the number of different micro states that correspond to that macro state So we saw three and five before there's only one micro state that gives you a sum of three But there are six different ways you can lay the dice out to get a sum of five And there are 27 different ways you can lay them out to get a sum of 10 And so this tells you what omega is and then if you just do the calculation stick it in your calculator The natural log and here's the most important thing about the natural log it goes up when the number goes up so more micro states Bigger log of number of micro states and then entropy remember is just a constant times that number more micro states Higher entropy so a higher entropy state is a state where there are more different ways you could rearrange particles In order to have that macro state So we've talked about dice now. I'm about to use the little question thing again So those of you who weren't here for the demo at the beginning Click on this box here that will give you something in your inventory It'll be a folder and then inside that folder. There'd be an object called qa hud In your inventory right click on it and select add and that should put on the lower left of your screen The letters a through f brightly colored. So go ahead and do that Because what I'm about to do is ask you a question and I want you to tell me what you think the answer is now I'm going to ask you not to discuss this in local chat because it's going to be very tempting to shout out Oh, it's this but what I want you to do is see can you get this without hearing what everybody else is so avoid um, spoiling the answer in local chat just go ahead and Click the answer that you think is right when I put the question up So I'm going to put the question up The click won't work until you see the question on your hud itself So here is the question I have a gas and this is a very rarefied gas because it only has 40 particles in it There's this microstate where here's 20 of the particles and here's 20 of the particles And here's another microstate where the 20 particles are all spread around which of these micro states Is more probable a or b or they equally probable or you have to know more about gas dynamics in order to answer the question So if it worked you should see the question on your hud now click a through d don't click e or f because that's not useful Which microstate is more probable? You don't see the question on your hud make sure you have the hud attached And um, yeah, if you right click on it and select add it should go onto your um screen And if you're not getting the question, I'm sorry, I don't know what's wrong I still I obviously still have to do some debugging with this Because it doesn't seem to be working for everybody All right, we're up to 18 answers Yeah, if SL is acting up it may give you trouble 19 answers 20 answers Um, at some point I'm going to close it off and we'll see what everybody said I don't know if you need to have the science circle tag. It should work anyway I don't think you need to be in the group either. It should work anyway Yeah, you can try a detaching and reattaching Um, when you reattach you may have to wait up to about five seconds before the question shows So when you attach it, there'll be no question Within five seconds the question should show up. Actually. All right, so I'm going to close it off We've got 21 answers. It seems to be pretty stable Let's see what people said Close the question. Let's go over and look at the results we got It didn't work Close question there we go um, all right well So here the answer has got pretty good most of you got the right answer the answer is c they are equally probable It's very tempting To say that b is more probable right because if I give you a gas a bunch of air molecules Which one is it more likely to look like is it more likely to look like this or this? Well It turns out it's equally likely to look like both of them and you say wait a minute You never see all of the air molecules on the gas collected into two corners of the room You never see that but you do see them kind of randomly spread throughout the room all the time Well, all right. Well, what's going on? Here's what's going on There's a whole bunch of different ways For the gas to be randomly sped around the room And here they are I've just I mean not all of them This is a tiny tiny fraction of the ways to spread around these 40 gas molecules in my little rectangle here I just randomly generated 20 is this 2015 I randomly generated 15 different distributions of gas and put them up here and here the randomly generated ones And notice if you look at them closely you can see they're different But overall they look pretty much the same. They're more or less evenly distributed They're kind of randomly spread throughout the whole thing and none of them Look like the one where they were all collected into two corners But each one of these microstates is just as likely As this one here Right. This is just as probable as this Just like when I roll three dice Um, and I get one one one It is just as probable as getting say two three five The difference is there's a whole bunch of different ways to have them kind of seemingly smeared around Whereas there's only a small number of ways to have them all collected just in two corners like this so this This is a low entropy macro state where the density profile is all of them here and all of them here This is a high entropy macro state because the density is pretty much uniform throughout at least if you Shmere if you defocus your eyes a little bit. It's pretty much uniform for out So all of these are pretty much uniform for out. Well I didn't actually force it to look. I just randomly chose states So there was a non-zero probability when I randomly generated these states that I would get All of the spots in the two corners. It's just that I didn't because the probability is so low because there's so few microstates like that So this is really this is really what entropy is about When we say entropy is disorder, it's just because what we think of is disordered There are way more ways to be what we think of as disordered than there are ways for us to be ordered Think about your sock drawer There are way more ways To have your sock drawer be a mess Then there is to have your sock drawer organized right take your sock drawer. That's a mess stir it up all the socks are in different places It's still a mess stir it up again. All the socks are in different places. It's still a mess If you organize your sock drawer Well, there's only a few things you can move a whole one pair of socks here and move the other pair of socks back But there's only a few things you can do without making it A mess and so when we think of something as a mess Well, generally we're just thinking of something that is there's a whole bunch of other Microstates that are very similar to it right now I want to throw one more random concept out and this is a nod to To vik we were discussing or phil vik slash one over root to vik plus one over root to phil We were discussing ahead of time what kind of scientist is phil And I think the answer is he's a scientist, but certainly he is a computer guy And um, there's another computer guy present gumby wonby over here. He's actually a philosopher. So don't trust him But one of he's he's a philosopher who's currently writing a book on quantum computation So he's one of those philosophers and when I mentioned that he's giving a talk on entropy Of course, the first thing he mentioned was information because that's what um That's what computer people think about with entropy is information um And you will hear entropy connected to information and how the heck does that work Well, we're going to go back to the dice the entropy of a system relates to how much information you can encode in that system and when I talk about encoding information Well, let's think about building an alphabet All right, so let's suppose My system is going to be all combinations of three dice and they're ordered so I can tell one die apart from the other There's died the you know the left one the middle one on the right one All combinations of three dice that give us a sum of five and I want to use that to build an alphabet Well, I can have six different letters in my alphabet because there's six different ways to lay down three dice that sum to five All right, and a six letter alphabet Well, it's going to be hard to build a lot of words in that But I guess what the hawaiian alphabet only has 12 or 13 letters I don't remember what it is and so, you know You can certainly get by with fewer letters than we are used to in our alphabets But okay, that's a six letter alphabet. That's great That in a sense tells you how much information there is And thank you Vic. It tells you how much information there is In one set of three dice that sum to five There's enough information to tell six different things apart from each other In contrast if instead of insisting that the three dice sum to five I said, let's let them sum to 10 There are 27 different combinations of dice and here they all are 27 different combinations of dice and this allows me to build an alphabet with 27 letters in it So I chose the 26 latin letters that most of us use and then because maybe somebody here is from germany I added the sharp s or the shroof or whatever you call this Funny looking thing that looks to me like a beta Um as the 27th letter because why not I had to choose something that was not One of the 26 that I usually use that's it I guess that's one way to call it sharp s is one thing I've heard it I've heard it called and that's what if I'll be perfectly honest If you go into the unicode encoding where I have it. I think it's called a sharp s Whatever. So the point is is that Remember that three dice who sum to 10 is a higher entropy state than three dice who sum to five Because there are more different microstates. Well If you let each of those microstates encode a letter you can encode more letters when the three dice sum to 10 Then you can win the three dice sum to five and so this Really broadly speaking is what it means when we talk about entropy and information being related to each other The more entropy you have in your system the more information it's possible To have in that system Now this goes a little bit at odds when you think about thermodynamics because wait a minute are high entropy states Random states where there's not useful information at anymore. It's like yes. Okay. So it's not exactly the same thing But If you have a system with lots of microstates and then somehow you have a way of forcing it into one of the other Microstate then yes, that is a way you can encode information And so people who do information theory will talk about the amount of entropy you have in fact sometimes They will use bits of entropy How many how many bits of entropy do you have? This is a term that you can look up If you search for the xkcd Horse battery staple correct Password comic and those of you who know what i'm talking about know what i'm talking about The rest of you assume I just said some things in a language you don't know You'll see here. He talks about bits of entropy. Well or bits of information In n bits So oops previous I wanted to click this slide Laser on there we go in n bits. There are two to n two to the n different numbers Like so for example, if you have one bit, there's only two different numbers It can be zero or one It's a computer and two to the one is two whereas two to the two is four And now you can have four different numbers zero zero zero one one zero and one one Two cubed is eight You now have eight different numbers and two to the fourth is 16 You now have 16 different numbers So the more bits you have the more different numbers you have and you could then go And make each one of these numbers say be a letter of your alphabet And now you're doing character encoding Here's the thing Notice I have two to the n is the amount of information. What is for it's called a nibble NYB BLE Is half of a bite. I don't know why I know that that's left over from when I was a kid Um, I don't think anyone uses that term anymore um Notice there's two to the n. We're raising something to a power and that is very Interesting because raising something to a power is the opposite operation of a logarithm If I take log base two of two to the n I get n Right remember I may have you may have heard me say before that Log base 10 is what number do you have to raise 10 to in order to get to the number? Well, two to the n so two to the three is eight the net the log base two Of eight is two Now we talked natural logarithms before Um, here's how you convert from natural logarithm to log base two if you really want to Um, but logarithm as a concept is what is important If you remember statistical mechanics definition of entropy was a constant times the natural log The log base two of eight is three. I'm sorry. I may have said that wrong the log base two of eight is three Um, it's a constant times the natural log of the number of microstates So the number of microstates is sort of like The number of bits And the more bits you have the more information you can encode. Well, okay There is a connection between entropy and information All right. Well, so I'm running out of time. So I'm going to jump on unfortunately. It's my last slide now summary What? Ah, yes Um Yeah, log base two of eight is three that is correct. I may have said it wrong the first time Summary what is entropy entropy is disorder? And I put a question mark because when somebody says entropy is disorder What do you mean? Challenge them. What do you actually mean by disorder and in particular being a physicist? I want a mathematical definition I want you to give me some math that you can connect to the concepts that I can then interpret and understand So that I can use the math as a mode of communication entropy is disorder. All right, that's great. How do you quantify that? What are you really talking about? Well Exclamation point because we've talked about that disorder. It's the number of different microstates. Yeah entropy is like porn You know it when you see it. No I mean it is true often you kind of know it when you see it but sometimes it can be a little deceptive But okay, we have a way of talking about what disorder means and that's this Um Bold red one later. I'll come back to that for another one the ability of a system to do Useful work. I know corn when I see it. It's yellow and it's on the cob um The ability to do use of a system to do useful work Well as entropy goes up the ability to useful work goes down So like the Gibbs free energy or something goes down Or the amount of thermal energy per unit temperature So just at a given temperature, how much energy do you have that you can extract as work the higher entropy you have The less thermal energy you can extract to do useful work So so these two definitions are actually The inverse of entropy but here is the fundamental physics definition. I gave you it's the logarithm Times a constant of the number of microstates available for the macro state of the system and again question I was like what that sounds like a whole bunch of double talk. He just used a whole bunch of big words Well, hopefully I gave you some sense with the dice of what it means to talk about a microstate in a macro state And that's the orange down here the number of ways you can rearrange all the particles in the system So if your system is three dice the number of ways I can have The three dice have different values showing and still have basically the same overall state So if we mean the same overall state that might mean okay where all the density is constant across the Room and all the temperature is constant across the room and what are the different number of ways I could rearrange all of the gas molecules and get that well There's a whole lot whereas there's not very many when they're all in the two corners So that is what entropy is and it is now one minute after 11. So I will stop here and take any residual Questions anybody has Thank you all. Thank you everybody Yeah, Newtonian mechanics. I mentioned before statistical mechanics and in a sense. Well, all right So Newtonian mechanics means use Newton's laws Um, Newton's laws together with Galilei and kinematics. So velocity and acceleration and then forces mass times acceleration um I don't think zero kelvin does mean zero entropy I think you can have more than zero entropy even at zero kelvin with a classical system All right, the universe will have infinite microsystems. In fact, it doesn't really have infinite microsystems And the reason is well first, uh, okay, unless the universe is infinite in which case it does and then there's parallel universes And it's really scary, but if we consider the observable universe Which is a mere 42 Billion light years across or something like that. So it's not that big um Turns out that there aren't an infinite number of states because of quantum mechanics because Particles are indistinguishable and because atoms have quantized energy states. The number is ginormous Outerly hugely ginormous, but there's actually not an infinite number of states There's only a finite a huge number, but finite number of ways to rearrange All those atoms Yeah, so does that all right. So an object at zero kelvin has zero thermal energy It could have potential energy But remember potential energy is the energy of how things interact with each other So I could have an object at zero k that's at rest Held over a gravitational field and it will have gravitational potential energy as a result um There is also the whole notion. Well, okay The truth is is that once you have quantum mechanics, it's impossible to get actually exactly to zero kelvin because Zero thermal energy is inconsistent with heisenberg uncertainty principle So that you're always going to have some little I mean you're always you can have zero kelvin But there's going to be some uncertainty about that So anyway, so anyway, so the universe doesn't really have an infinite number of systems, but It's still a really good question if you have an infinite number of different microstates. How do you calculate it? It turns out these 40 particles in a box already have an infinite number of microstates Because each particle could be at any position and I could however far I move one particle I could always move it half as far and I could move it half as far as that So there's an infinite number of different positions a particle could be at so how do we handle that? Well, we handle that What do you do when you have zero you divide by zero? We handle it by choosing some sort of smallest size And what is that smallest size? Well, actually we usually motivate it by quantum mechanics and use the Planck's constant which is about the size of uncertainties in quantum mechanics, and then we do integrals and And then it all works out is what ends up happening. So there are ways to handle it The math is just a little more advanced to deal with continuous systems. What about in indeterminacy? So that adds a whole bunch of richness to the whole thing indeterminacy You know, there can be entropy associated with various indeterminate states Indeterminacy can also I mean that sort of sets Among other things a minimum scale for when you can meaningfully talk about two things Being at the same place or not because of the heisenberg uncertainty principle and all of that quantum mechanics And another thing about indeterminacy is if you have two different particles and quantum mechanics, they're both electrons You can't tell them apart It's like dice where you can't tell which die is which So one die having three and the other having one is exactly the same thing as the first one having one And the second one having three so um In quantum mechanics indistinguishable particles changes the statistics, but the basic idea of entropy stays the same Yeah, so what mike said there's going to be various potential chemical potential energies that if you have Um carbon 12 different atoms in different places even though they're all perfectly at rest There's still some you could in principle by rearranging them somehow get energy out So that will be a potential energy How can we so zero entropy this basically systems are never in zero entropy The only way to have zero entropy is if there is only one microstate possible Um, and that's never going to happen if you have a system where entropy is a meaningful concept Entropy is only a meaningful concept once you have enough particles Um that it's worth talking about it's sort of like temperature Temperature is the av is related to the average um Random motion kinetic energy of particles if you have one particle What is the average of one particle? Well, it's the same as that one particle But why talk about average when you only have one thing? All right. Well, I am going to wander off Um, thank you all for coming and thank you for participating in both my dice experiment and my Uh clicker hut experiment. I'm gonna have to think about See if I can figure out why a few people seem to have trouble with the clicker hut Um, I'm probably gonna have to get a bunch of people Together to test this while I'm editing it and it'll be very boring for them But um, or I should just log in a whole bunch of bots to test it I'll figure something out. Anyway, thank you all for coming and I will see you all again in the future Goodbye everyone